Analytical models for fast-ion beam-target fusion spectra in magnetized plasmas

Thermonuclear fusion plasmas offer a promising route to efficient, low-impact electricity generation. Among several existing and proposed approaches, magnetic-confinement fusion currently appears the most mature. Although the burning-plasma era remains out of reach, predictive experiments and modelling can be carried out on smaller and/or lower-field devices. This transitional phase is essential for advancing our understanding of the physics at play. In particular, energetic particles are not only intrinsic to fusion plasmas, as they are born from fusion reactions and are generated by external heating, but also proven to significantly affect the performance of experiments. They may damage the machine by escaping confinement, nonlinearly interact with magnetohydrodynamic instabilities, and even positively affect turbulence. Crucially, theoretical and numerical modelling of energetic-particle physics can be improved by validation against measurements. We pursue this validation via forward modelling, designing algorithms that compare energetic-particle data with synthetic signals computed from their distribution functions.

In this work, we refine computational techniques for neutron and gamma-ray emission spectroscopy by reducing the underlying velocity-space models to fully analytical forms. This yields faster execution and more explicit formulations of spectrum generation. The reduction is achieved by enforcing the beam–target approximation, in which the fast reactant is fully modelled while the slow one is assumed at rest. This assumption has modest, controlled effects on predicted neutron spectra, whereas gamma-ray spectra show minimal to no discrepancy relative to standard Monte-Carlo methods that sample the full phase space. Furthermore, we extend the velocity-space model for two-step gamma-ray spectroscopy to the phase space of guiding-center orbits and compute corresponding weight functions. This enables the inclusion of spatial effects at low dimensionality and the rapid computation of spectra from arbitrary distributions. Notably, two-step gamma-ray spectroscopy will be important for detecting confined alpha particles in future devices.